Best Known (82, 114, s)-Nets in Base 9
(82, 114, 760)-Net over F9 — Constructive and digital
Digital (82, 114, 760)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 18, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (64, 96, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 48, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 48, 370)-net over F81, using
- digital (2, 18, 20)-net over F9, using
(82, 114, 5898)-Net over F9 — Digital
Digital (82, 114, 5898)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9114, 5898, F9, 32) (dual of [5898, 5784, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(9114, 6570, F9, 32) (dual of [6570, 6456, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(29) [i] based on
- linear OA(9113, 6561, F9, 32) (dual of [6561, 6448, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(9105, 6561, F9, 30) (dual of [6561, 6456, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(31) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(9114, 6570, F9, 32) (dual of [6570, 6456, 33]-code), using
(82, 114, 5350887)-Net in Base 9 — Upper bound on s
There is no (82, 114, 5350888)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 6 076399 338058 008033 700815 838036 920516 145931 872727 317873 924766 960506 617796 841349 504185 820443 635247 645271 378945 > 9114 [i]